Solve ax=x+9/x^2-2x-48

$$a x = \frac { x + 9 } { x ^ { 2 } - 2 x - 48 }$$

Solve for a

$$a=\frac{x+9}{x\left(x-8\right)\left(x+6\right)}$$

$$x\neq -6\text{ and }x\neq 8\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-8\right)\left(x+6\right).

$$ax\left(x-8\right)\left(x+6\right)=x+9$$

Use the distributive property to multiply ax by x-8.

$$\left(ax^{2}-8ax\right)\left(x+6\right)=x+9$$

Use the distributive property to multiply ax^{2}-8ax by x+6 and combine like terms.

$$ax^{3}-2ax^{2}-48ax=x+9$$

Combine all terms containing a.

$$\left(x^{3}-2x^{2}-48x\right)a=x+9$$

Divide both sides by x^{3}-2x^{2}-48x.

$$\frac{\left(x^{3}-2x^{2}-48x\right)a}{x^{3}-2x^{2}-48x}=\frac{x+9}{x^{3}-2x^{2}-48x}$$

Dividing by x^{3}-2x^{2}-48x undoes the multiplication by x^{3}-2x^{2}-48x.

$$a=\frac{x+9}{x^{3}-2x^{2}-48x}$$

Divide x+9 by x^{3}-2x^{2}-48x.

$$a=\frac{x+9}{x\left(x-8\right)\left(x+6\right)}$$